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Let's break down and solve both problems from the image you uploaded.

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### **Problem 9**

**Given:**
- An aquarium contains 6 female fish and 3 male fish.
- You are to catch a male fish, then a female fish, then another male fish, replacing each fish after every catch.

**Solution:**

Since the fish are replaced after each catch, the events are independent, and we can multiply the probabilities of each event happening in sequence.

- Probability of catching a male fish:  
  \[
  \frac{\text{Number of male fish}}{\text{Total number of fish}} = \frac{3}{9} = \frac{1}{3}
  \]
- Probability of catching a female fish:  
  \[
  \frac{\text{Number of female fish}}{\text{Total number of fish}} = \frac{6}{9} = \frac{2}{3}
  \]
- Probability of catching another male fish:  
  \[
  \frac{3}{9} = \frac{1}{3}
  \]

Thus, the total probability is:
\[
\frac{1}{3} \times \frac{2}{3} \times \frac{1}{3} = \frac{2}{27}
\]

So, the answer is **A. 2/27**.

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### **Problem 10**

**Given:**
- A bag contains 5 red marbles, 3 yellow marbles, and 2 blue marbles. Once a marble is drawn, it is **not replaced**.
- You need to find the probability of drawing **two red marbles** in a row.

**Solution:**

Since the marbles are not replaced, the events are **dependent**. We calculate the probability of each event step by step.

- Total marbles = \( 5 + 3 + 2 = 10 \)

- Probability of drawing a red marble on the first draw:  
  \[
  \frac{5}{10} = \frac{1}{2}
  \]
- After drawing the first red marble, there are 4 red marbles left and a total of 9 marbles left in the bag. So, the probability of drawing a second red marble:  
  \[
  \frac{4}{9}
  \]

Thus, the total probability is:
\[
\frac{1}{2} \times \frac{4}{9} = \frac{4}{18} = \frac{2}{9}
\]

So, the answer is **C. 2/9**.

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### Do you want more details on any of these steps or have any questions?

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Here are five related questions for practice:

1. What is the probability of catching two female fish in a row (with replacement) from the aquarium in problem 9?
2. What is the probability of drawing one yellow marble followed by one blue marble without replacement in problem 10?
3. If you catch three fish without replacement, how does the probability change in problem 9?
4. What would be the probability of drawing a red and a blue marble (in that order) without replacement from problem 10's bag?
5. How does the probability change if the events were independent in problem 10?

**Tip:** In probability problems, pay close attention to whether events are dependent or independent, as this significantly affects the calculations.

An aquarium contains 6 female fish and 3 male fish. What is the probability of catching a male fish, then a female fish, and then another male fish, if you put each fish back in the aquarium before catching another one? A bag contains 5 red marbles, 3 yellow marbles, and 2 blue marbles. Once a marble is drawn, it is not replaced. What is the probability of drawing two red marbles?

Solve two probability problems: calculating the chances of catching specific fish from an aquarium (with replacement) and drawing two red marbles from a bag (without replacement). These problems explore independent and dependent probability scenarios.

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